Related papers: Lipschitz Singularities in Diffusion Models
This study explores the integration of Blackout Diffusion into the DIFUSCO framework for combinatorial optimization, specifically targeting the Traveling Salesman Problem (TSP). Inspired by the success of discrete-time diffusion models…
Diffusion and flow matching models have achieved remarkable success in text-to-image generation. However, these models typically rely on the predetermined denoising schedules for all prompts. The multi-step reverse diffusion process can be…
Accelerating diffusion model sampling is crucial for efficient AIGC deployment. While diffusion distillation methods -- based on distribution matching and trajectory matching -- reduce sampling to as few as one step, they fall short on…
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
Accelerated diffusion models hold the potential to significantly enhance the efficiency of standard diffusion processes. Theoretically, these models have been shown to achieve faster convergence rates than the standard $\mathcal…
The development of video diffusion models unveils a significant challenge: the substantial computational demands. To mitigate this challenge, we note that the reverse process of diffusion exhibits an inherent entropy-reducing nature. Given…
Diffusion models (DMs) have revolutionized generative learning. They utilize a diffusion process to encode data into a simple Gaussian distribution. However, encoding a complex, potentially multimodal data distribution into a single…
Diffusion models have demonstrated remarkable capabilities in text-to-image and text-to-video generation, opening up possibilities for video editing based on textual input. However, the computational cost associated with sequential sampling…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be…
We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Using techniques from stochastic thermodynamics, we derive…
Zero-shot, training-free, image-based text-to-video generation is an emerging area that aims to generate videos using existing image-based diffusion models. Current methods in this space require specific architectural changes to image…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
We develop a finite-dimensional sensitivity framework for studying stability in learning systems whose states include representations, parameters, and update variables. The central object is the \emph{Learning Stability Profile}, a…
In this paper, we consider the inverse problem of recovering a diffusion and absorption coefficients in steady-state optical tomography problem from the Neumann-to-Dirichlet map. We first prove a Global uniqueness and Lipschitz stability…
Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…
We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient. We prove tightness and the Feller property of…
Generative learning, recognized for its effective modeling of data distributions, offers inherent advantages in handling out-of-distribution instances, especially for enhancing robustness to adversarial attacks. Among these, diffusion…
Discrete diffusion models offer a promising alternative to autoregressive generation through parallel decoding, but they suffer from a sampling wall: once categorical sampling occurs, rich distributional information collapses into one-hot…